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Find the values of the unknowns x and y in the following diagrams:

2. Find the values of the unknowns x and y in the following diagrams

        

  

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i) As we know, the exterior angle is equal to the sum of opposite internal angles in a triangle.

50^0+x=120^0

x=120^0-50^0

x=70^0

Now, As we know the sum of internal angles of a triangle is 180. so,

50^0+x+y=180^0

50^0+70^0+y=180^0

y=180^0-50^0-70^0

y=60^0

Hence, x=70^0\:\:and\:\:y=60^0.

ii)  As we know when two lines are intersecting, the opposite angles are equal. So

y=80^0

Now, As we know the sum of internal angles of a triangle is 180. so,

50^0+y+x=180^0

50^0+80^0+x=180^0

x=180^0-50^0-80^0

x=50^0

Hence, x=50^0\:\:and\:\:y=80^0.

iii) As we know, the exterior angle is equal to the sum of opposite internal angles in a triangle

x=50^0+60^0

x=110^0

Now, As we know the sum of internal angles of a triangle is 180. so,

y+50^0+60^0=180^0

y=180^0-50^0-60^0

y=70^0

Hence, x=110^0\:\:and\:\:y=70^0.

iv) 

As we know when two lines are intersecting, the opposite angles are equal. So

x=60^0

Now, As we know the sum of internal angles of a triangle is 180. so,

30^0+y+x=180^0

30^0+y+60^0=180^0

y=180^0-30^0-60^0

y=90^0

Hence, x=60^0\:\:and\:\:y=90^0

v) As we know when two lines are intersecting, the opposite angles are equal. So

y=90^0

Now, As we know the sum of internal angles of a triangle is 180. so,

y+x+x=180^0

90^0+2x=180^0

2x=90^0

x=45^0

Hence, x=45^0\:\:and\:\:y=90^0

vi)As we know when two lines are intersecting, the opposite angles are equal. So

y=x

Now, As we know the sum of internal angles of a triangle is 180. so,

x+x+x=180^0

3x=180^0

x=60^0

Hence, x=60^0\:\:and\:\:y=60^0.

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